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In this article, we propose a parametric model for the distribution of time to first event when events are overdispersed and
can be properly fitted by a Negative Binomial distribution. This is a very common situation in medical statistics, when the
occurrence of events is summarized as a count for each patient and the simple Poisson model is not adequate to account for
overdispersion of data. In this situation, studying the time of occurrence of the first event can be of interest. From the
Negative Binomial distribution of counts, we derive a new parametric model for time to first event and apply it to fit the
distribution of time to first relapse in multiple sclerosis (MS). We develop the regression model with methods for covariate
estimation. We show that, as the Negative Binomial model properly fits relapse counts data, this new model matches quite perfectly
the distribution of time to first relapse, as tested in two large datasets of MS patients. Finally we compare its performance,
when fitting time to first relapse in MS, with other models widely used in survival analysis (the semiparametric Cox model
and the parametric exponential, Weibull, log-logistic and log-normal models). 相似文献
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